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AuthorGuermond, Jean-Luc (6)Popov, Bojan (4)Guermond, J.-L. (2)Pasquetti, Richard (2)Bangerth, Wolfgang (1)View MoreJournalComputer Methods in Applied Mechanics and Engineering (2)Journal of Computational Physics (2)SIAM Journal on Numerical Analysis (2)SIAM Journal on Scientific Computing (2)Computational Mechanics (1)View MoreKAUST Grant NumberKUS-C1-016-04 (11)KUK-C1-013-04 (1)PublisherElsevier BV (7)Society for Industrial & Applied Mathematics (SIAM) (4)American Mathematical Society (AMS) (1)EDP Sciences (1)Springer Nature (1)Subject

Finite elements (14)

Conservation laws (2)Discontinuous Galerkin (2)Entropy viscosity (2)Euler equations (2)View MoreTypeArticle (14)Year (Issue Date)2015 (2)2013 (3)2012 (1)2011 (4)2010 (3)View MoreItem AvailabilityMetadata Only (14)

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A correction technique for the dispersive effects of mass lumping for transport problems

Guermond, Jean-Luc; Pasquetti, Richard (Computer Methods in Applied Mechanics and Engineering, Elsevier BV, 2013-01) [Article]

This paper addresses the well-known dispersion effect that mass lumping induces when solving transport-like equations. A simple anti-dispersion technique based on the lumped mass matrix is proposed. The method does not require any non-trivial matrix inversion and has the same anti-dispersive effects as the consistent mass matrix. A novel quasi-lumping technique for P2 finite elements is introduced. Higher-order extensions of the method are also discussed. © 2012 Elsevier B.V.

An Efficient Implicit FEM Scheme for Fractional-in-Space Reaction-Diffusion Equations

Burrage, Kevin; Hale, Nicholas; Kay, David (SIAM Journal on Scientific Computing, Society for Industrial & Applied Mathematics (SIAM), 2012-01) [Article]

Fractional differential equations are becoming increasingly used as a modelling tool for processes associated with anomalous diffusion or spatial heterogeneity. However, the presence of a fractional differential operator causes memory (time fractional) or nonlocality (space fractional) issues that impose a number of computational constraints. In this paper we develop efficient, scalable techniques for solving fractional-in-space reaction diffusion equations using the finite element method on both structured and unstructured grids via robust techniques for computing the fractional power of a matrix times a vector. Our approach is show-cased by solving the fractional Fisher and fractional Allen-Cahn reaction-diffusion equations in two and three spatial dimensions, and analyzing the speed of the traveling wave and size of the interface in terms of the fractional power of the underlying Laplacian operator. © 2012 Society for Industrial and Applied Mathematics.

Asymptotic Analysis of Upwind Discontinuous Galerkin Approximation of the Radiative Transport Equation in the Diffusive Limit

Guermond, Jean-Luc; Kanschat, Guido (SIAM Journal on Numerical Analysis, Society for Industrial & Applied Mathematics (SIAM), 2010-01) [Article]

We revisit some results from M. L. Adams [Nu cl. Sci. Engrg., 137 (2001), pp. 298- 333]. Using functional analytic tools we prove that a necessary and sufficient condition for the standard upwind discontinuous Galerkin approximation to converge to the correct limit solution in the diffusive regime is that the approximation space contains a linear space of continuous functions, and the restrictions of the functions of this space to each mesh cell contain the linear polynomials. Furthermore, the discrete diffusion limit converges in the Sobolev space H1 to the continuous one if the boundary data is isotropic. With anisotropic boundary data, a boundary layer occurs, and convergence holds in the broken Sobolev space H with s < 1/2 only © 2010 Society for Industrial and Applied Mathematics.

Effects of discontinuous magnetic permeability on magnetodynamic problems

Guermond, J.-L.; Léorat, J.; Luddens, F.; Nore, C.; Ribeiro, A. (Journal of Computational Physics, Elsevier BV, 2011-07) [Article]

A novel approximation technique using Lagrange finite elements is proposed to solve magneto-dynamics problems involving discontinuous magnetic permeability and non-smooth interfaces. The algorithm is validated on benchmark problems and is used for kinematic studies of the Cadarache von Kármán Sodium 2 (VKS2) experimental fluid dynamo. © 2011 Elsevier Inc.

Error Analysis of a Fractional Time-Stepping Technique for Incompressible Flows with Variable Density

Guermond, J.-L.; Salgado, Abner J. (SIAM Journal on Numerical Analysis, Society for Industrial & Applied Mathematics (SIAM), 2011-01) [Article]

In this paper we analyze the convergence properties of a new fractional time-stepping technique for the solution of the variable density incompressible Navier-Stokes equations. The main feature of this method is that, contrary to other existing algorithms, the pressure is determined by just solving one Poisson equation per time step. First-order error estimates are proved, and stability of a formally second-order variant of the method is established. © 2011 Society for Industrial and Applied Mathematics.

Implementation of the entropy viscosity method with the discontinuous Galerkin method

Zingan, Valentin; Guermond, Jean-Luc; Morel, Jim; Popov, Bojan (Computer Methods in Applied Mechanics and Engineering, Elsevier BV, 2013-01) [Article]

The notion of entropy viscosity method introduced in Guermond and Pasquetti [21] is extended to the discontinuous Galerkin framework for scalar conservation laws and the compressible Euler equations. © 2012 Elsevier B.V.

Entropy viscosity method for nonlinear conservation laws

Guermond, Jean-Luc; Pasquetti, Richard; Popov, Bojan (Journal of Computational Physics, Elsevier BV, 2011-05) [Article]

A new class of high-order numerical methods for approximating nonlinear conservation laws is described (entropy viscosity method). The novelty is that a nonlinear viscosity based on the local size of an entropy production is added to the numerical discretization at hand. This new approach does not use any flux or slope limiters, applies to equations or systems supplemented with one or more entropy inequalities and does not depend on the mesh type and polynomial approximation. Various benchmark problems are solved with finite elements, spectral elements and Fourier series to illustrate the capability of the proposed method. © 2010 Elsevier Inc.

Finite element discretization of Darcy's equations with pressure dependent porosity

Girault, Vivette; Murat, François; Salgado, Abner (ESAIM: Mathematical Modelling and Numerical Analysis, EDP Sciences, 2010-02-23) [Article]

We consider the flow of a viscous incompressible fluid through a rigid homogeneous porous medium. The permeability of the medium depends on the pressure, so that the model is nonlinear. We propose a finite element discretization of this problem and, in the case where the dependence on the pressure is bounded from above and below, we prove its convergence to the solution and propose an algorithm to solve the discrete system. In the case where the dependence on the pressure is exponential, we propose a splitting scheme which involves solving two linear systems, but parts of the analysis of this method are still heuristic. Numerical tests are presented, which illustrate the introduced methods. © 2010 EDP Sciences, SMAI.

Maximization of wave motion within a hydrocarbon reservoir for wave-based enhanced oil recovery

Jeong, C.; Kallivokas, L.F.; Kucukcoban, S.; Deng, W.; Fathi, A. (Journal of Petroleum Science and Engineering, Elsevier BV, 2015-05) [Article]

© 2015 Elsevier B.V. We discuss a systematic methodology for investigating the feasibility of mobilizing oil droplets trapped within the pore space of a target reservoir region by optimally directing wave energy to the region of interest. The motivation stems from field and laboratory observations, which have provided sufficient evidence suggesting that wave-based reservoir stimulation could lead to economically viable oil recovery.Using controlled active surface wave sources, we first describe the mathematical framework necessary for identifying optimal wave source signals that can maximize a desired motion metric (kinetic energy, particle acceleration, etc.) at the target region of interest. We use the apparatus of partial-differential-equation (PDE)-constrained optimization to formulate the associated inverse-source problem, and deploy state-of-the-art numerical wave simulation tools to resolve numerically the associated discrete inverse problem.Numerical experiments with a synthetic subsurface model featuring a shallow reservoir show that the optimizer converges to wave source signals capable of maximizing the motion within the reservoir. The spectra of the wave sources are dominated by the amplification frequencies of the formation. We also show that wave energy could be focused within the target reservoir area, while simultaneously minimizing the disturbance to neighboring formations - a concept that can also be exploited in fracking operations.Lastly, we compare the results of our numerical experiments conducted at the reservoir scale, with results obtained from semi-analytical studies at the granular level, to conclude that, in the case of shallow targets, the optimized wave sources are likely to mobilize trapped oil droplets, and thus enhance oil recovery.

On phase transformation models for thermo-mechanically coupled response of Nitinol

Sengupta, Arkaprabha; Papadopoulos, Panayiotis; Kueck, Aaron; Pelton, Alan R. (Computational Mechanics, Springer Nature, 2011-03-31) [Article]

Fully coupled thermomechanical models for Nitinol at the grain level are developed in this work to capture the inter-dependence between deformation and temperature under non-isothermal conditions. The martensite transformation equations are solved using a novel algorithm which imposes all relevant constraints on the volume fractions. The numerical implementation of the resulting models within the finite element method is effected by the monolithic solution of the momentum and energy equations. Validation of the models is achieved by means of thin-tube experiments at different strain rates. © 2011 Springer-Verlag.

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